Apologies for the delay in a response. I've never heard of the specific charge that Seneca the Younger was the first investment banker per se, but I can cite several of the historical accounts that may have justified such a monicker. Both Tacitus and Cassius Dio, in covering Seneca, noted the accusation of making his fortune through charging high interest rates on expensive loans.

In one such instance, the Senator Publius Suillius Rufus accused Seneca of making his fortune through this practice, as well as sleeping with Agrippina among other charges. Suillius Rufus would go on to be succesfully prosecuted by Seneca in response, resulting in the loss of half of his property (per Tacitus' Annales). In another instance, Cassius Dio would also link the practice of making such loans with the eventual uprising of Boudica. Reportedly, Seneca lent money to local aristocrats and then proceeded to call them in aggressively, which prompted the outbreak of the revolt.

Though both accounts may be subject to some degree of skepticism (especially given the existing context of their treatment of Nero's reign), there is likely some truth to Seneca's sensitivity or awareness of these allegations, as he specifically defends both gaining and spending wealth in De Vita Beata.

While Seneca's behavior might be somewhat similar to an investment banker today (more so in leveraged finance vs. M&A, though I'd argue this is more akin to a credit investor than anything else), he is far from the first person, or the first major historical figure, to engage in this type of lending.

On this, there are actually a variety of interesting contemporary accounts of the Financial Crisis of 33 CE that mention the practice that I can recommend (I believe these are also mentioned by Tacitus, but I can confirm this fully if you have any follow-ups on this episode): https://epicenter.wcfia.harvard.edu/blog/financial-crisis-then-and-now